Question

Satellite this is for you!
ax^2+bx+c

Answer 1

factor?

Answer 2

yes
to split the middles
you find two factors of a*c whose product is a*c that add up to be b
say the two factors of a*c=m*n and m+n=b
just replace bx=mx+nx

Answer 3

it was bothering me

Answer 4

\[a(x-\frac{-b+\sqrt{b^2-4ac}}{2a})(x-\frac{-b-\sqrt{b^2-4ac}}{2a})\]

Answer 5

lol eww

Answer 6

do you just not like "spilty" or do you not know how to do it

Answer 7

i really have no idea.

Answer 8

completing the square always works

Answer 9

x^2+5x+6
x^2+2x+3x+6
x(x+2)+3(x+2)
(x+2)(x+3)

4x^2+8x+3
4x^2+6x+2x+3
2x(2x+3)+(2x+3)
(2x+3)(2x+1)

Answer 10

two examples

Answer 11

so for the 5 i was looking for two numbers that add to 5 and whose product is 6? this is just regular factoring yes?

Answer 12

yes
what about the second one
what did i do?

Answer 13

lets see... produce of ac is 12

Answer 14

so you split 8 as 2 + 6 ?

Answer 15

omg my little satellite is growing up

Answer 16

yes easy!

Answer 17

yeah just took my training wheels off!

Answer 18

but quad formula never fails
well for quadratics (a does not equal)

Answer 19

except for that one hair had who said we were limited on the ways we could approach one problem

Answer 20

do you member it?
i remember something about square root

Answer 21

yes and you can complete the square too. sometime called "sophie germain"

Answer 22

sophie whos that?

Answer 23

is she hotter than me i wonder

Answer 24

for example
factor
\[x^4+4\]

Answer 25

no she is dead since 1831

Answer 26

and pretended to be a man to study math!

Answer 27

(x^2+2i)(x^2-2i)
you guys are sexist
and i guess we can factor this further

Answer 28

so to factor \[x^4+4\] rewrite as
\[x^4+2x^2+4-2x^2\]

Answer 29

oh no not over complex. watch!

Answer 30

hey satellite if these times were like those times would you let me do work and you publish it?

Answer 31

ok go ahead

Answer 32

yes, after you did the dishes

Answer 33

and made you a sandwich?

Answer 34

that too. and fetched a beer. ok i think i made a mistake it is
\[x^4+4=x^4+4x^2+4-4x^2\]

Answer 35

you know my cat can do math and i publish his work under my name becasue you know we don't allow them to talk

Answer 36

now you have the difference of two squares it is
\[(x^2+2)^2-4x^2\]

Answer 37

so you factor as
\[(x^2+2x+2)(x^2-2x+2)\]

Answer 38

oh! i think this is pretty

Answer 39

very cute

Answer 40

try it with
\[x^4+x^2+1\]

Answer 41

putting me on the spot how sweet

Answer 42

hint is what would you add to make that a perfect square

Answer 43

lol ok

Answer 44

...

Answer 45

x^4+2x^2+1+x^2-2x^2
=(x^2+1)^2-x^2
=(x^2+1-x)(x^2+1+x)

Answer 46

i am impressed

Answer 47

works for factoring trinomials as well, although can be cumbersome

Answer 48

and if the leading coefficient is not one you have to work with fractions (heaven forbid)

Answer 49

i can do math withoust sleep
i haven't slept
i been watching this show about british/australian teenagers who turn into mermaids whenever they touch water

Answer 50

lol

Answer 51

i saw that you were here early in the morning east coast time. must have been up very late

Answer 52

http://en.wikipedia.org/wiki/Sophie_Germain
i dont know she looks pretty sexy to me

Answer 53

she has a witch nose

Answer 54

i want to make math spells and magic

Answer 55

ok maybe i should go to sleep before i embarrassed myself

Answer 56

good night!

Answer 57

good morning

Answer 58

its 10:43 am

Answer 59

thanks for teaching me something it was nice